• 1 Katedra Matematike

Various properties of the Mellin transform function$$\mathcal{M}_k(s):= \int_1^{\infty} Z^k(x)x^{-s}\,dx$$are investigated, where $$Z(t):=\zeta(\frac{1}{2}+it)\,\chi(\frac{1}{2}+it)^{-1/2},~~~~\zeta(s)=\chi(s)\zeta(1-s)$$is Hardy's function. Connections with power moments of $|\zeta(\frac{1}{2}+it)|$ are established, and natural boundaries of $\mathcal{M}_k(s)$ are discussed.